Fourier analysis on polytopes and the geometry of numbers, part I : a friendly introduction
Robins, Sinai
Fourier analysis on polytopes and the geometry of numbers, part I : a friendly introduction - India : Universities Press, 2025. - xxiii, 325 pages - Student mathematical library, v. 107 1520-9121 ; .
Includes bibliographical references and index.
This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class.
Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
Readership: Undergraduate and graduate students and researchers interested in analysis and periodical structures.
9789349750517
Fourier analysis
Polytopes
Geometry of numbers
Geometry--Real and complex geometry--Polyhedra and polytopes
Number theory--Additive number theory
Convex and discrete geometry--Polytopes and polyhedra
Geometry of numbers--Lattice packing and covering
514.113.5 / ROB-F
Fourier analysis on polytopes and the geometry of numbers, part I : a friendly introduction - India : Universities Press, 2025. - xxiii, 325 pages - Student mathematical library, v. 107 1520-9121 ; .
Includes bibliographical references and index.
This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class.
Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.
Readership: Undergraduate and graduate students and researchers interested in analysis and periodical structures.
9789349750517
Fourier analysis
Polytopes
Geometry of numbers
Geometry--Real and complex geometry--Polyhedra and polytopes
Number theory--Additive number theory
Convex and discrete geometry--Polytopes and polyhedra
Geometry of numbers--Lattice packing and covering
514.113.5 / ROB-F
